TOPIC
MY PROGRESS
Pug Score
0%
Best Streak
0 in a row
Study Points
+0
Overview
Practice
Watch
Read
Quiz
Next Steps
Get Started
Get unlimited access to all videos, practice problems, and study tools.
Back to Menu
Topic Progress
Pug Score
0%
Videos Watched
0/0
Best Practice
No score
Read
Not viewed
Best Quiz
No attempts
Best Streak
0 in a row
Study Points
+0
Overview
Practice
Watch
Read
Quiz
Next Steps
Overview
Continuous Growth and Decay Formula
Understand the continuous growth and decay formula and see how it models continuous compound interest and real-world change over time.
What You'll Learn
Continuous growth and decay describe quantities that change at every instant rather than in discrete steps, modeled by A equals P times e to the power of r t.
The constant e (about 2.71828) appears because continuous compounding is the limit of compounding more and more frequently.
A positive rate r gives continuous growth, while a negative rate r gives continuous decay, in the same formula.
Continuous compound interest is the most common real-world use of this formula, applied to money, population, and radioactive decay problems.
Graphing the formula produces the familiar exponential curve, rising for growth and falling toward zero for decay.
What You'll Practice
1
Computing account balances with continuous compound interest over many years
2
Finding decay rates of radioactive substances given half-life
3
Using natural logarithms to solve for variables in exponents with base e
4
Interpreting continuous growth and decay in real-world contexts
Why This Matters
Continuous growth and decay models are essential for understanding real-world phenomena like compound interest, population growth, and radioactive decay. This formula appears throughout advanced math, physics, chemistry, and finance, making it crucial for STEM careers and higher-level coursework.
Before You Start — Make Sure You Can:
This Unit Includes
2 Video lessons
Practice exercises
Learning resources
Skills
Exponential Growth
Exponential Decay
Continuous Compounding
Natural Logarithm
Half-Life
Euler's Number
Interest Rate Calculations
NS Curriculum Aligned